`y=tan^(-1)((acosx-bsinx)/(bcosx+asinx)),w h e r e-pi/2<x<pi/2a n d a/btanx >-1`

Question

`y=tan^(-1)((acosx-bsinx)/(bcosx+asinx)),w h e r e-pi/2-1`

Answer 1

`"Let "y=tan^(-1)((a cos x- b sin x)/(b cos x + a sin x)),`
`=tan^(-1)(((a)/(b)-tan x)/(1+(a)/(b) tan x))`
`=tan^(-1)((a)/(b))-tan^(-1)(tan x)`
`=tan^(-1)((a)/(b))-x" "[because-(pi)/(2)ltxlt(pi)/(2)`
`therefore" "(dy)/(dx)=0-1=-1`